I used to think Newton’s method was a bit old-school. Turns out I was the one playing catch-up. This is about Newton’s method and a clever way to make it work for constrained optimization. Consider optimizing an unconstrained function $f(\cdot)$ whose Hessian exists. Newton’s method works around its gradient function, finding a point $x^\star$ such that $\nabla f(x^\star) = 0$. In an iterative way, at each point $x^k$, it approximates the gradient function $\nabla f(\cdot)$ around $x^k$ using its second-order derivative information $$ \nabla {\tilde f}(x^{k + 1}) \approx \nabla f(x^k) + \nabla^2 f(x^k)(x^{k + 1} - x^k), $$ and solve for $x^{k + 1}$ such that this approximation equals zero—which gives us the classic update: $$ x^{k + 1} = x^k - (\nabla^2 f(x^k))^{-1}\nabla f(x^k)....

Best known for his intimate, almost translucent interpretations of Debussy and Ravel, Gieseking’s style has long divided listeners. Some dismiss his playing as emotionally distant or overly plain (me). But others say it’s a refusal to overstate (almost me). Like, take his Debussy as an example—most pianist lean into impressionism drama. Eg., the master of which: Gieseking’s moonlight is like, wind whisper through water. He lets those notes hang like breath and his pedaling is nearly, invisible....

May 25th is part of the annual Mental Health Awareness Month—today encourages individuals to focus on their own well-being. And I got insomnia…is that contagious? Anyway, if the night caught you sober—might as well stay here just a little longer and let’s listen to Chopin together. Here’s Nocturne Op. 9 No. 1—let our thoughts becomes feelings and feelings become sky.

Wine pairs with food. A good book pairs with music too. This weekend I’ve been hypnotized by Nabokov’s Lolita (for academic purposes, thank you). It’s strange, obsessed and beautifully written—like something dark wrapped in silk. It goes too well with Szymanowski’s Myths (Op 30). The music is dreamy, intense, and just a little unsettling. It feels like it mirrors the book’s mood—especially in the first half, when everything still seems elegant, restrained on the outside....

I used to think first-order methods (FOM) were mostly just warm-up materials. But after sitting through Professor Ye’s lightning-fast 3-hour tour of the topic… FOM are probably the best! I can’t do a full overview of FOMs here. Here are some takeaways from the lecture: a few highlights that are surprisingly insightful and fun so worth pausing over. We’ll skip zero-order methods. Sure, you can do bisection (aka binary search) if you assume strong structure on the objective function....

Jony Ive has really good taste. Now, will OpenAI also have good taste? (Basicallly, Jony Ive was in charge of Apple’s design—iPhone4S, Apple Watch, iPad, Macbook—the crazily trendy minimalistic silver look. He created and led this omnipresent minimalist fashion that influenced and infiltrated into EVERYTHING.) And now Jony Ive teams up with OpenAI. The news is all over the internet. Interestingly it somewhat looks like a planned marketing campaign. When I searched “Jony Ive San Altman” on Google, an ads pop up:...

OMG. USC, UCLA team up for the world’s first-in-human bladder transplant Keck Medicine of USC. https://news.keckmedicine.org/usc-ucla-team-up-for-the-worlds-first-in-human-bladder-transplant/ Dr Inderbri Gill from USC and Nima Nassiri from UCLA—jointly completed a bladder transplantation surgery to a patient who has been on dialysis for seven years. He lost the majority of his bladder during surgery to resect cancer over five years ago, leaving the remainder of his bladder too small and compromised to function appropriately....

My advisor calls it a classic first-world problem… But if a beautifully written article can uncork curiosity in wine lovers and get them swirling the issue of climate change around their minds — isn’t that progress, one pour at a time? Lara Williams from bloomberg has this excellent opinion article about climate change affecting Champagne quality: Is Champagne’s Bubble About to Burst? TL;DR: warming temperatures makes grapes to ripe ealier and aggregates more sugar....

Hedwig’s Theme is a leitmotif composed by John Williams for the film adaptation of Harry Potter and the Philosopher’s Stone. While not exclusively written for the character, it is better known for being the main theme of every Harry Potter film and is iconic for the wizarding world in general. (Harry Potter Wiki) John Williams with the Berliner Philharmoniker in 2022, recorded by Deutsche Grammonphon Check out the Hedwig’s theme below:...

(Recall previously when we wrote about the Sweetener philosophy): it’s kind of about bringing light to a situation or to someone’s life or somebody else brings light to your life, “sweetening the situation” —Ariana Grande Lately, I’ve been revisiting Harry Potter and the Prisoner of Azkaban. There’s one particular quote in the movie that resonates deeply: Albus Dumbledore Happiness can be found even in the darkest of times, if one only remembers to turn on the light...